Stress-Induced Phase Transformations in Shape-Memory Polycrystals

Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound, and the extent of phase transformation is given by the constant strain Taylor bound. Finally we discuss the stress–strain relations of the general problem using Milton–Serkov bounds

Constitutive modeling of metastable austenitic stainless steel

A stress-update algorithm is developed for austenitic metastable steels which undergo phase evolution during deformation. The material initially comprises only the soft and ductile austenite phase which due to the phenomenon of mechanically induced martensitic transformation, transforms completely to the hard and brittle martensite. A mean-field homogenization algorithm is developed that can predict the mechanical response of the composite material during transformation. Furthermore, a physically based transformation model is developed that predicts the amount of transformation during deformation